ABC is a triangle The bisectors of the internal angle ang B and external angle ang C intersect at D ...........

Quantitative Aptitude ( CCS) Geometry

ABC is a triangle. The bisectors of the internal angle ∠B and external angle ∠C intersect at D. if ∠BDC = 50°, then ∠A is

100°

90°

120°

60°

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Explanation:

We know that, Exterior angle is sum of opposite interior angles
∴ ∠ACE = ∠A + ∠ABC
⇒ 2y = ∠A + 2x
⇒ ∠A = 2y – 2x ...(i)
Similarly,
∠DCE = ∠DBC + ∠BDC
⇒ y = x + 50°
From equation (i)
∠A = 2(x + 50°) – 2x
= 2x + 100° – 2x = 100°